scholarly journals A Review of Procedures for Summing Kapteyn Series in Mathematical Physics

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
R. C. Tautz ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Mathematical Physics ◽  
Short Review ◽  
Quantum Systems ◽  
Review Article ◽  
Functional Behavior ◽  
Basic Physics ◽  
Kapteyn Series ◽  
Physics Problems

Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.

Solving functions in the mathematical physics problems

PAMM ◽  
2003 ◽  
Vol 2 (1) ◽  
pp. 356-357
Author(s):  
M. J. Al-Khatib ◽  
R. Leśniewska
Keyword(s):  
Mathematical Physics ◽  
Physics Problems

ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

2007 ◽  
Vol 05 (03) ◽  
pp. 291-299
Author(s):  
MOURAD E. H. ISMAIL
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Entire Functions

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

scholarly journals Political Anthropology and Anthropology of Politics: An Overview

2012 ◽  
Vol 5 ◽  
pp. 217-234
Author(s):  
Suresh Dhakal
Keyword(s):  
Historical Development ◽  
Cultural Anthropology ◽  
Short Review ◽  
Review Article ◽  
Political Transition ◽  
Political Anthropology ◽  
The Political ◽  
Cultural Processes ◽  
Recent Trends ◽  
Anthropology Of Politics

In this short review, I have tried to sketch an overview of historical development of political anthropology and its recent trends. I was enthused to prepare this review article as there does not exist any of such simplified introduction of one of the prominent sub-fields in cultural anthropology for the Nepalis readers, in particular. I believe this particular sub-field has to offer much to understand and explain the recent trends and current turmoil of the political transition in the country. Political anthropologists than any other could better explain how the politics is socially and culturally embedded and intertwined, therefore, separation of the two – politics from social and cultural processes – is not only impossible but methodologically wrong, too. DOI: http://dx.doi.org/10.3126/dsaj.v5i0.6365 Dhaulagiri Journal of Sociology and Anthropology Vol. 5, 2011: 217-34

scholarly journals Similarities between Hurricanes and Galaxies: A Short Review

2021 ◽  
Author(s):  
Jim Henry ◽  
Mesut Yurukcu ◽  
George Nnanna
Keyword(s):  
Milky Way ◽  
Spiral Galaxies ◽  
Spiral Structure ◽  
Fibonacci Numbers ◽  
Short Review ◽  
Review Article ◽  
Double Spiral ◽  
Natural Pattern

Universe created with the fundamental laws of science. Nature is lazy and needs to form with the least possible to be perfect. A natural pattern, such as pinecones, sunflowers, pineapples, and cacti, has a double spiral structure. Once we look at these plants' centers, we will see the seeds line up in spirals shape. The number of spirals whirling in each direction will give us the Fibonacci numbers. We can give more examples representing these natural patterns; however, one example is unique and remarkable. The similarities between spiral galaxies- Milky Way and hurricanes. Are they similar in every property or just in shape and rotational movements? What are the similarities between them? This short review article will try to find these questions' answers by reviewing some literature articles. The first part of this article gave some information about hurricanes and galaxies. The second of this article focused on the comparison between hurricanes and galaxies. Finally, we will conclude the article with our remarks.

scholarly journals Quantum Calcium-Ion Interactions with EEG

Sci ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Stochastic Systems ◽  
Analytic Solution ◽  
Short Term Memory ◽  
Mathematical Physics ◽  
Modest Improvement ◽  
Classical Physics ◽  
Arbitrary Time ◽  
Eeg Data

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

QUANTUM DISCORD UNDER SYSTEM–ENVIRONMENT COUPLING: THE TWO-QUBIT CASE

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345054 ◽  
Author(s):  
JIN-SHI XU ◽  
CHUAN-FENG LI
Keyword(s):  
Quantum Discord ◽  
Open Quantum Systems ◽  
Short Review ◽  
Quantum Systems ◽  
External Control ◽  
Control Effect ◽  
Fundamental Physics ◽  
System Environment ◽  
Open Quantum ◽  
Distinct Property

Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system–environment dynamics of two-qubit quantum discord and the influence of initial system–environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.

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